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Langmuir 2007, 23, 6660-6666
Choose Sides: Differential Polymer Adhesion Lars Sonnenberg,*,† Julien Parvole,‡ Ferdinand Ku¨hner,† Laurent Billon,‡ and Hermann E. Gaub† Lehrstuhl fu¨r Angewandte Physik and Center for NanoScience, Ludwig-Maximilians-UniVersita¨t Mu¨nchen, Amalienstr. 54, 80799 Mu¨nchen, Germany, and Laboratoire de Physico-Chimie des Polyme` res, UniVersite´ de Pau et des pays de l’Adour, He´ lioparc Pau-Pyre´ ne´ es, 2 AV Pre´ sident Angot, 64053 Pau Cedex 09, France ReceiVed December 20, 2006. In Final Form: February 13, 2007 AFM-based single molecule desorption measurements were performed on surface end-grafted poly(acrylic acid) monolayers as a function of the pH of the aqueous buffer to study the adhesion properties of polymers that bridge two surfaces. These properties were found to depend on the adhesion forces of both surfaces in a differential manner, which is explained with a simple model in analogy to the Bell-Evans formalism used in dynamic force spectroscopy. The measured interaction forces between the poly(acrylic acid) chains and silicon nitride AFM tips depend on the grafting density of the polymer monolayers as well as on the contour length of the polymer chains. This study demonstrates that the stability of polymer bridges is determined by the adhesion strengths on both surfaces, which can be tuned by using pH-dependent polyelectrolyte monolayers.
Introduction The adhesion of polymers to solid surfaces is of central importance for many technological applications. Thereby, polyelectrolyte molecules are of special interest since their water solubility promises economical and ecological benefits. In adhesives not only does the interaction with one surface count, but the polymers have to bridge two surfaces, which may be of a different nature. Differential adhesion aspects may dominate here! The two surfaces compete for the polymer to adhere, which eventually may result in a situation where adhesion is strong but bridging is lost. From the scientific point of view, the adsorption of charged molecules to charged surfaces is far from being completely understood as long-range Coulomb interactions play an important role and among other things complex charge regulation mechanisms occur.1,2 The atomic force microscope (AFM) has been shown to be a powerful tool to study the adhesion of single polymer molecules on solid supports by force spectroscopy measurements.3-7 Therein single polyelectrolyte (PEL) molecules were continuously desorbed from a solid surface, and the corresponding desorption force was analyzed. Interestingly, the molecules show a high lateral mobility on the surface and simultaneously a high adsorption energy on the order of 10-20 kBT,8 a combination of adhesion properties with particular relevance for polymer coatings. The studies investigating the polyelectrolyte desorption from solid supports showed that the desorption force can be measured * Corresponding author. † Ludwig-Maximilians-Universita ¨ t Mu¨nchen. ‡ Universite ´ de Pau et des pays de l’Adour. (1) Netz, R. R.; Andelman, D. Phys. Rep. 2003, 380, 1-95. (2) Dobrynin, A. V.; Rubinstein, M. Prog. Polym. Sci. 2005, 30, 1049-1118. (3) Chatellier, X.; Senden, T. J.; Joanny, J. F.; di Meglio, J. M. Europhys. Lett. 1998, 41, 303-308. (4) Hugel, T.; Grosholz, M.; Clausen-Schaumann, H.; Pfau, A.; Gaub, H.; Seitz, M. Macromolecules 2001, 34, 1039-1047. (5) Seitz, M.; Friedsam, C.; Jo¨stl, W.; Hugel, T.; Gaub, H. E. Chem. Phys. Chem. 2003, 4, 986-990. (6) Friedsam, C.; Becares, A. D.; Jonas, U.; Seitz, M.; Gaub, H. E. New J. Phys. 2004, 6. (7) Cui, S. X.; Liu, C. J.; Wang, Z. Q.; Zhang, X. Macromolecules 2004, 37, 946-953.
reproducibly and with high precision. However, as the measured desorption force is only depending on the interaction of the polymer with the surface from which it is desorbed, differential aspects of the adhesion cannot be monitored. Instead, the appropriate experimental parameter to monitor the competition of the two surfaces is the length of the bridging segment as it is directly correlated with the lengths of the surface adsorbed segments. Here we show that the adsorption properties of polymer chains bridging two surfaces are dependent on the adhesion forces of both surfaces. In detail, the adhesion strength between end-grafted poly(acrylic acid) (PAA) chains and silicon nitride (Si3N4) AFM tips was modulated via a pH variation of the aqueous solution. As a result, the measured bridging length is increased or decreased, respectively. In order to explain the experimentally observed correlation of bridging length and desorption force, we present a model in analogy to the Bell-Evans formalism used in dynamic force spectroscopy. The measured pH-dependence of the desorption force resembles the pH-dependent degree of dissociation of the PAA chains. We show that the density of polymer chains on the surface has an effect on the obtained desorption forces and thus on the dissociation equilibrium. In addition, the desorption forces were found to depend on the contour length of the polymer chains. Materials and Methods Surface End-Grafted Poly(acrylic acid) Monolayers. The synthesis and chemical characterization of surface end-grafted poly(acrylic acid) (PAA) monolayers as used in this study is described in detail in refs 9 and 10. In brief, the “grafting-from technique” was used to prepare the PAA (-CH2CHCOOH-)n monolayers. The polymerization initiator was covalently bound via monochlorosilane headsgroups to the inorganic substrate (silicon wafer) and the PAA chains were synthesized under controlled/living radical polymerization conditions. The grafting density was afterward adjusted by (8) Ku¨hner, F.; Erdmann, M.; Sonnenberg, L.; Serr, A.; Morfill, J.; Gaub, H. E. Langmuir 2006, 22, 11180-11186. (9) Sonnenberg, L.; Parvole, J.; Borisov, O.; Billon, L.; Gaub, H. E.; Seitz, M. Macromolecules 2006, 39, 281-288. (10) Parvole, J.; Montfort, J. P.; Reiter, G.; Borisov, O.; Billon, L. Polymer 2006, 47, 972-981.
10.1021/la063682y CCC: $37.00 © 2007 American Chemical Society Published on Web 05/10/2007
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Figure 1. (a) Schematics of a single molecule desorption experiment with surface end-grafted polymers by means of an AFM. (b) Typical records of the de-adhesion force measured upon retracting the tip from the surface. A plateau represents a polymer sliding off the tip. The number of plateaus equals the number of desorbed polymer chains. (c) Statistical analysis of the bridging length lbr and the desorption force FA. The distribution of the bridging length is a function of the molecular length distribution of surface-grafted chains. The histogram of the desorption force can be fit by a Gaussian distribution with typical values for fwhm of ca. 6 pN. Histograms were taken from the “dilute” monolayer at pH 6. partial cleavage of the PAA chains from the surface. An ester group that connects the initiator and the silane anchor group acts herein as a break-seal group. Gel permeation chromatography (GPC) and X-ray photoelectron spectroscopy (XPS) were applied to the samples to determine the molecular weight of the PAA chains and to estimate their grafting density on the surface. This characterization opens up the possibility to directly compare GPC and AFM results obtained on the same samples. In the following, it is referred to two PAA monolayer samples, which are for differentiation named “dense” (D) and “dilute” (d). The PAA chains from the “dense” monolayer have an average contour length of 〈lc〉D ≈ 590 nm and a polydispersity of PDD ) 1.3. The “dilute” sample consists of PAA chains with an average contour length 〈lc〉d ≈ 450 nm and PDd ) 1.24. The grafting densities were estimated as follows: σD ≈ 0.005 molecule/nm2 ≈ 2.3σd. AFM Desorption Experiments. In AFM-based desorption measurements using end-grafted polymer monolayers, single polymer chains are adsorbed on the tip of an AFM cantilever and successively desorbed from the tip by separating the AFM tip and sample surface (see Figure 1). With these experiments, we are able to probe a
Langmuir, Vol. 23, No. 12, 2007 6661 multitude of polymers grafted from a flat surface with the very same tip as follows: When approaching a bare AFM tip the chains will adsorb on the AFM tip as they gain adsorption enthalpy. Upon retraction of the AFM tip, the polymers successively desorb in an equilibrium process, which is due to a much faster dynamics of the surface-polymer contacts in comparison to the retraction velocity of the AFM tip (ca. 1 µm/s). The polymers are not pinned to the AFM tip but highly mobile; that is, the adsorbed polymer segment is able to slide on the tip surface.8 This means that the heterogeneities of the tip surface are not reflected in the measured force as the polymer rearranges during the desorption in order to maximize its adsorption enthalpy. The corresponding force-distance curves thus show plateaus of constant force representing the desorption process. As the complete desorption of a polymer chain is indicated by a drop in force, the number of desorbed molecules equals the number of observed plateaus, and the absolute distance at which a force drop occurs states the bridging length lbr. At high adsorption strengths, the polymer chain stays adsorbed until the end segment detaches, and the bridging length therefore represents the contour length of the polymer. Lateral displacements of the grafting point on the sample surface and the tip apex shorten the bridging length in comparison to the contour length of the polymer chain. However, in the case of contour lengths on the order of several hundred nanometers as used here (i.e., at length scales much larger than the end-to-end distance of the polymer chains), this effect becomes negligible. The height of the force plateau represents the magnitude of the desorption force between the PEL chain and the surface, the mean desorption force is obtained by a statistical analysis. The desorption force histograms typically show values for the full width at halfmaximum (fwhm) of ca. 6 pN, which enables a determination of the desorption forces with 1-2 pN precision. The analysis of the desorption forces is a bit more complicated here as the desorption forces are slightly dependent on the bridging length. From one measurement series, all plateaus are analyzed in terms of bridging length, but only the last plateau is considered for the desorption force as here no intermolecular interaction can adulterate the polymersurface interaction. The desorption force is then taken from the bridging length that corresponds to the maximum position of the bridging length distribution. All desorption experiments were conducted with a custom-made instrument using silicon nitride (Si3N4) cantilevers (Microlever) purchased from Veeco Instruments. Nominal spring constants were calibrated using the thermal oscillation method.11 Note that the calculated spring constants may have deviations of up to 10%; therefore, measurements series were performed with the same cantilever for being able to monitor minute force differences. Before the measurements, the Si3N4 tips were cleaned with UV light, and control measurements on the interaction of the AFM tips with bare silica substrates were performed in order to exclude contaminations of the tip surface. In the desorption experiments, only these bare Si3N4 tips were used. The experiments were conducted in aqueous solution containing 100 mM NaCl, and typically at least 1000 force-distance curves were measured on different spots on the surface to ensure that a representative ensemble of molecules is probed.
Theoretical Basis Differential Polymer Adhesion Model. In a desorption experiment as described above, the PEL chain is not only able to interact with the AFM tip but also with the sample surface on which the polymers are grafted (see Figure 2). The resulting competition of the two surfaces for the polymer to adhere affects the measured bridging length. In contrast to that, the measured desorption force is only depending on the interaction of the polymer molecule with the desorbing surface. In the case of an AFM tip in the vicinity of the sample surface, the molecule will only adsorb onto the tip surface when it is (11) Butt, H. J.; Jaschke, M. Nanotechnology 1995, 6, 1-7.
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Figure 3. Calculated probability density functions p(d) for distinct values of the difference in adsorption forces ∆F ) FA - FS according to the proposed model for differential polymer adhesion. The adsorbed length is set to 590 nm, the attempt frequency to 108 s-1 and the retraction velocity to 1 µm/s.
Figure 2. Model for differential polymer adhesion showing the adsorption energy vs the distance d of the two surfaces. The polymer chain is grafted at surface S and allowed to interact with both surfaces, A and S. Only if the adsorption force of A (FA) is higher than the adsorption force of S (FS), the polymer chain will adsorb on A with the length lads. When successively desorbing the polymer chain from A, the adsorption energy is reduced proportional to FA until the equilibrium distance deq is reached at which the adsorption energy of the remaining adsorbed segment equals the adsorption energy if the polymer would be completely adsorbed on S. Thus, from this distance on it is energetically not favorable for the adsorbed polymer segment to stay adsorbed at A. The system is now in a metastable state. Thermal fluctuations may detach the remaining adsorbed segment and as a consequence, the measured (bridging) length becomes dependent on the difference of the adsorption forces between both surfaces.
energetically favorable. In a simple perception, the adhesion force of the polymer chain with the AFM tip FA (which equals the adhesion enthalpy per unit length) has to exceed the adhesion force with the substrate FS. The length of the polymer chain, which then adsorbs on the AFM tip is denoted by lads. When retracting the AFM tip, monomers of the polymer chain are successively desorbed from the AFM tip surface and the overall adsorption energy is reduced proportional to FA. However, at a certain tip-substrate separation d, which here is called the equilibrium distance deq, the equilibrium adsorption enthalpies of the remaining adsorbed segment on the AFM tip and of the polymer chain completely adsorbed on the substrate are equal: deq ) (1 - FS/FA)lads. When further enlarging the tip-substrate separation, d, the continuous desorption from the tip is energetically not favorable to the complete detachment of the remaining adsorbed segment from the AFM tip any more. Nevertheless, this metastable desorption of monomers from the tip is still likely as the two states are separated by an energy barrier, which has to be overcome by thermal fluctuations. The probability that the system manages to overcome the energy barrier is thereby increased by further desorbing monomers from the AFM tip as the height of the energy barrier is proportional to the number of adsorbed monomers. In this distance regime, d > deq, a nonequilibrium process next to the continuous desorption process under equilibrium conditions has to be considered: the instantaneous and complete detachment of the adsorbed part of the polymer chain from the AFM tip. In the framework of a two-state model comprising an adsorbed and a detached conformation, the instantaneous complete detachment of the adsorbed polymer segment can be treated in close analogy to the dissociation process known for example
from breaking ligand-receptor bonds. Thus, a model in analogy to the Bell-Evans formalism12,13 widely used in dynamic force spectroscopy is proposed here (see Figure 2). It is therein assumed that the dissociation process is determined by the difference in adsorption forces of the two surfaces ∆F ) FA - FS. The distancedependent thermal off-rate koff is then given as
koff(d) ) k0 exp
(
(d - lads)∆F kBT
)
(1)
with the attempt frequency k0, the length of the adsorbed polymer lads, and the thermal energy kBT. The probability function P(d) for the detached state is then given by
(
P(d) ) 1 - exp -
1 ν
∫dd koff(l) dl)
(2)
0
wherein V ) dd/dt describes the retraction velocity of the AFM tip during the experiment, which is experimentally adjusted. The probability density function p(d), which describes the probability to find a detachment event at a distance d, becomes
p(d) )
dP(d) koff(d) 1 ) exp dd ν ν
(
∫dd koff(l) dl)
(3)
0
The probability density function of the surface-grafted polymer monolayer can in principle be directly adjusted to the measured distribution of bridging lengths. Therefore, the following parameters have to be determined: the adsorbed length lads, the attempt frequency k0, and the adsorption force of the polymer with the substrate FS. FA representing the interaction of the molecule with the AFM tip is directly measured in the experiment as it is given by the height of the force plateau in the forcedistance curves. A calculation of the probability density function for distinct values of ∆F is given in Figure 3, wherein lads ) 590 nm, k0 ) 108 s-1, and V ) 1 µm/s are assumed. These values correspond to the average length of a polymer chain in the “dense” monolayer, the retraction velocity used in the experiments, and the time scale of fluctuations of a Kuhn segment in a polymer chain (1-10 ns).14,15 It can be seen that a notable decrease of the bridging length only occurs if the adsorption forces of the two surfaces are quite similar. Already at a force difference ∆F ) 4 pN the bridging length resembles the adsorbed length lads. Moreover, a decrease (12) Evans, E.; Ritchie, K. Biophys. J. 1997, 72, 1541-1555. (13) Bell, G. I. Science 1978, 200, 618-627. (14) Kimmich, R.; Fatkullin, N. AdV. Polym. Sci. 2004, 170, 1-113. (15) Tang, J.; Lin, S. H. Phys. ReV. E 2006, 73.
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Figure 4. Length shift ∆l as obtained with desorption measurements at varying pH in dependence of the measured desorption force FA. The correlation of the two parameters is qualitatively in very good agreement with formula 4, when FS is considered constant.
in bridging length is associated with a broadening of the probability density function. An average bridging length 〈lbr〉 can be defined as the maximum position of the probability density function p(d) or the measured distribution of bridging lengths, respectively
〈lbr〉 )
( )
kBT ν∆F + lads ) ∆l + lads ln ∆F k0kBT
(4)
In conclusion, the bridging length is expected to shorten in comparison to lads when the adhesion forces of both surfaces become similar. The shortening of the bridging length is in the following also denoted as length shift ∆l < 0.
Results and Discussions Correlation between Desorption Force and Bridging Length. The aim of this section of the paper is to compare the experimental results with the proposed differential polymer adhesion model (i.e., to point out that differential aspects due to the simultaneous interaction of the polymer with two surfaces have to be considered). For the modeling according to eq 4, a shift ∆l of the measured bridging length has to be observed. This can be achieved by varying the pH of the aqueous solution because the electrostatic properties of PAA as a weak polyelectrolyte can be tuned by the solution pH.9 The most important prerequisite of the proposed model is a correlation between the length shift ∆l and the difference in desorption forces of both surfaces ∆F. From the experimental point of view ∆F is unknown and only the desorption force FA can be directly measured in the experiments. Thus, in Figure 4 the length shift ∆l ) 〈lbr〉 - lads is displayed versus the corresponding desorption force FA as observed at different pH values of an aqueous solution. Each data point of Figure 4 is based on a measurement series of about 1000 force-distance curves (see also Figure 1). Moreover data gained from two PAA monolayers of different grafting densities are shown. For both samples, the observed bridging lengths are an increasing function of the desorption force. Two main regimes can be distinguished as follows: In the case of pronounced length shifts (∆l < -50 nm), small variations of the desorption force have large impact on the length shift, whereas for small length shifts (∆l > -50 nm), ∆l is getting less sensitive to an increase of the desorption force. The dependence of the length shift on the desorption force is in very good agreement with the predictions of the model. The solid lines in Figure 4 are calculated curves based on formula 4 assuming a pH-independent FS of 63.4 pN for the “dilute” and
Figure 5. Distributions of bridging lengths for (a) the “dilute” and (b) the “dense” PAA monolayer. Both measurement series show a length shift of ∆l ≈ -140 nm. The fit of the bridging length were obtained by assuming the distribution of adsorbed lengths (dashed line) and applying the differential adhesion model. An attempt frequency of 108 s-1 and a force difference of ca. 0.5 pN is used in both cases.
66.8 pN for the “dense” sample. An attempt frequency of k0 ) 108 s-1 was used. These results already show that polymer bridging is a differential process comprising both surfaces as the bridging length is a function of the interaction force. The validity of the proposed model can be further tested because a length shift should go hand in hand with a broadening of the measured bridging length distribution (see Figure 3). This broadening should be most pronounced for large length shifts. Thus, in Figure 5, the bridging length distributions for the maximal observed length shift of ∆l ≈ -140 nm as obtained with the “dilute” and the “dense” PAA monolayer are displayed. In addition the distributions of adsorbed lengths are displayed (dashed lines in Figure 5), which correspond according to the definition to ∆l ≈ 0 nm. The distribution of adsorbed lengths and its correlation with the molecular length distribution of the PAA monolayer is discussed in detail in a separate study (manuscript in preparation). On the basis of eq 3, length distributions can be calculated and directly compared to the measured distributions of bridging lengths. Thereby, two model parameters have to be taken into account: the attempt frequency k0 and the force difference between the two surfaces ∆F. In the following, an attempt frequency of k0 ) 108 s-1 was assumed and ∆F remained the only fit parameter. The best agreement of the resulting calculations (solid lines in Figure 5) and the bridging length histogram was found for ∆F ≈ 0.5 pN in both cases. This observation is qualitatively in agreement with the proposed model as a similar value for ∆l has to be associated with a similar value for ∆F. This very good agreement between model and experiment shows that the model described above is a good approximation for differential aspects of polymer adhesion. pH-Dependent Desorption Forces. The main advantage of AFM-based desorption measurements is the quantification of
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Figure 6. Desorption forces as obtained with Si3N4 tips and the “dilute” and “dense” PAA monolayer in dependence on the solution pH. Errors bars represent the fwhm of the force histograms. Both data sets were fit with a titration function (solid lines). The two measurement series were taken with different AFM tips. To take small force differences due to the spring constant calibration into account, the desorption forces were adjusted such that the fit functions overlay at pH 3.
the interaction between polymer and surface with very high precision and the possibility to resolve various contributions to the desorption force (e.g., from electrostatic interactions4,5). In this section of the paper, we use this strength to conclude the pH-dependent charge density of the PAA chains from the desorption forces as a function of the solution pH. In general, the desorption force of a charged polymer on a charged surface consists of a Coulomb and a non-Coulomb contribution. The electrostatic desorption force Fel is in DebyeHu¨ckel approximation given as Fel ∝ κ-1στ with the Debye screening length κ-1, the surface potential σ, and the linear charge density of the polyelectrolyte chain τ. When the surface and polymer charges originate from dissociable ionic groups as in the case of PAA and silicon nitride, both σ and τ are pH-dependent. In addition, charge regulation has to be taken into account; that is, the degree of dissociation depends on electrostatic screening due to intramolecular Coulomb repulsion between adjacent charges.16-18 In Figure 6, the desorption forces measured with Si3N4 tips on the “dense” and “dilute” PAA monolayer are plotted versus the pH of the aqueous solution. Desorption forces decrease with increasing pH, the decrease is more pronounced in the case of the “dilute” sample. Both data sets can be fit with a titration function FA ) FA0 + ∆FA/(1 + 10pH-pK*) showing deflection points pK* ) 8.4 for the “dense” monolayer and pK* ) 6.0 for the “dilute” monolayer. A larger pK* value in the case of the “dense” PAA monolayer is in qualitative agreement with the proposed model of differential adhesion as the bridging length also decreases at higher pH for the “dense” monolayer (data not shown). It should further be noted that with the “dilute” sample at pH < 6 additional desorption forces were obtained that are significantly smaller than expected from the titration behavior (points χ1 and χ2 in Figure 6). The decrease of the desorption force with increasing pH value can be explained with increasing electrostatic repulsion of the negatively charged PAA chain and the negatively charged tip surface (the pK of the surface OH groups is around 2-3). The electrostatic desorption force is negative in the case of Coulomb repulsion and therefore lowers the overall desorption force when Coulomb interactions are increased. The observed behavior in (16) Friedsam, C.; Gaub, H. E.; Netz, R. R. Europhys. Lett. 2005, 72, 844850. (17) Boroudjerdi, H.; Kim, Y. W.; Naji, A.; Netz, R. R.; Schlagberger, X.; Serr, A. Phys. Rep. 2005, 416, 129-199. (18) Netz, R. R. J. Phys.: Condens. Matter 2003, 15, S239-S244.
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Figure 6 is most probably strongly correlated with the pHdependent dissociation of the carboxylic groups in the PAA chains as the typical titration function associated with dissociation reactions is able to reproduce the data. However, as the surface charge of the AFM-tip may also be increased with increasing pH, the deflection points pK* of the titration fits do not necessarily correspond to the apparent pK of the PAA chains. The difference of the pK* values in dependence on the grafting density of chains on the sample surface may be explained by Coulomb interactions between adjacent charges. It is well-known that the electrostatic repulsion between charges along the polyelectrolyte chain counters the dissociation reaction of the ionic groups. The apparent pK value of a PAA chain is therefore larger than the pK of a single carboxylic group. One may speculate that the electrostatic repulsion between neighboring PAA chains also lowers the molecules’ degree of dissociation. This intermolecular electrostatic repulsion should be absent for isolated polymer chains and should increase with increasing grafting density. For the “dilute” and “dense” PAA monolayer separated polymers and overlapping molecules are expected when a 3d conformation of the polymer chains on the surface is assumed. In this model, intermolecular interactions would lower the degree of dissociation of the polymer chains in the “dense” sample, whereas intermolecular electrostatic repulsion would be mainly negligible in the “dilute” sample. This would result in a grafting density dependent pK* value. However, it should be noted that this is most probably not true any more for higher grafting densities in the regime of dense polyelectrolyte brushes.19,20 At this point, it is important to emphasize that the considerations above did not include the impact of the AFM tip. The PAA chains adsorb on the tip surface as they gain free enthalpy. Thereby, the degree of dissociation of the adsorbed polymer might be affected: As soon as the polymer adsorbs on the AFM tip, the molecule is isolated and its dissociation is not dependent any more on the conformation in the polymer monolayer. As a consequence, the charge density of the polymer will probably be increased. However, once the PAA chain is adsorbed on the negatively charged tip surface, an increase in polymer charge density would lead to an increased Coulomb repulsion and thus to a reduction of the overall adsorption enthalpy. From the results displayed in Figure 6, we therefore conclude that the polymer tries to maximize its adsorption enthalpy such that a reduced dissociation of the PAA due to the conformation on the sample surface is conserved upon adsorption on the silicon nitride AFM tip. That is, the degree of dissociation of the adsorbed PAA polymer resembles the degree of dissociation of the polymer in the monolayer before adsorption on the tip. As a consequence, conclusions on the dissociation equilibrium of polyelectrolytes in a monolayer can be drawn from the desorption forces as obtained with AFM-based single molecule force spectroscopy. In the following, a comment on the very different desorption forces that were found for the “dilute” PAA monolayer at pH < 6 (points χ1 and χ2) is given. Most importantly in the context of this work, the observed bridging lengths that correspond to the very different desorption forces are in perfect agreement with the proposed model for differential polymer adhesion. A high/low desorption force results in a large/small bridging length. A very similar observation was made on the “dense” monolayer, namely a bimodal bridging length distribution was observed at (19) Ahrens, H.; Forster, S.; Hehn, C. A.; Kumar, N. A.; Naji, A.; Netz, R. R.; Seidel, C. J. Phys. Chem. B 2004, 108, 16870-16876. (20) Ru¨he, J.; Ballauff, M.; Biesalski, M.; Dziezok, P.; Gro¨hn, F.; Johannsmann, D.; Houbenov, N.; Hugenberg, N.; Konradi, R.; Minko, S.; Motornov, M.; Netz, R. R.; Schmidt, M.; Seidel, C.; Stamm, M.; Stephan, T.; Usov, D.; Zhang, H. N. AdV. Polym. Sci. 2004, 165, 79-150.
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Figure 8. Desorption forces FA as a function of the bridging length lbr (see insets of Figure 7) were fit according to FA ) F0 + (dFA/ dlbr)lbr. The values of the obtained slopes dFA/dlbr are plotted versus the mean desorption force FA.
Figure 7. Force-distance curves from different regimes of desorption forces (see scale in Figure 6): (a) was extracted from data of the “dilute” PAA monolayer, (b and c) from “dense” PAA monolayer data. The desorption forces FA in dependence of the bridging lengths lbr are shown in the insets.
pH 4 and 5.9 It was discussed that water becomes a bad solvent for PAA in this pH regime and that theoretical studies predict a coexistence of collapsed and noncollapsed chain conformations under this conditions.21,22 Contour Length Dependent Desorption Forces Analyzed at the Level of Individual Polymers. The conceptual strength of single molecule experiments is the option to sort data according to certain criteria and to achieve information that might be hidden in the ensemble averaging of bulk experiments. In this section of the paper we make extensively use of this option, since in addition to the ensemble properties discussed above, minute differences in the desorption forces were found on the level of individual PAA molecules. First of all it should be noted that the observed contour length dependent effects are minute effects, differences of the desorption (21) Raphael, E.; Joanny, J. F. Europhys. Lett. 1990, 13, 623-628. (22) Zhulina, E. B.; Borisov, O. V.; van Male, J.; Leermakers, F. A. M. Langmuir 2001, 17, 1277-1293.
force are just on the order of a few pN. Expressed in terms of adhesion enthalpy these differences correspond to less than 0.5 kBT per monomer. In Figure 7, force-distance curves are shown, which were sorted according to the desorption forces (see scale in Figure 6). The curves in Figure 7a were taken from “dilute” PAA monolayer data and represent the case of “low” desoprtion forces. Flat plateaus were observed for all bridging lengths, whereas the desorption force was found to increase with bridging length. This is most visible in the inset where the individual desorption plateau forces were extracted from the curves and plotted wih the dependence of the bridging lengths. In Figure 7b, curves from the “intermediate” force regime and the “dense” PAA monolayer are shown. Therein the plateau force was found to be constant (see inset Figure 7b). At “high” desorption forces, which correspond from the discussion above to uncharged polymer chains, a second effect occurs. In the curves in Figure 7c observed with the “dense” PAA monolayer, it can be seen that the desorption force decreases during the desorption process. In this case, the plateau forces seem to overlay at zero distance. The desorption forces in dependence on the bridging lengths as shown in the insets of Figure 7 were fit with a linear regression, FA ) F0 + (dFA/dlbr)lbr. Figure 8 shows the values of the obtained slopes dFA/dlbr plotted versus the mean desorption forces (see Figure 6). The slopes, which represent the magnitude of the contour length dependent effect on the desorption forces, are decreasing continuously with desorption force. The observed length dependent desorption force may be explained by contour length dependent variation of the degree of dissociation. If the force decrease as displayed in Figure 6 is related to enhanced electrostatic interactions, the Coulomb repulsion is most pronounced at “low” desorption forces (Figure 7a). Contour-length dependent effects that are caused by a slightly varying degree of dissociation should best be visible in this force regime. The results from Figure 7a would then be interpreted with a slightly decreasing degree of dissociation of PAA chains with increasing contour length as was also observed with titration experiments.23 If the argument of contour length dependent polymer charge densities holds true, this effect has to attenuate when the electrostatic interaction is decreased (i.e., at higher desorption forces). This is what we observe as continuous decrease of this effect as illustrated in Figure 8 until it is not detectable any more (see Figure 7b). However, at higher desorption forces, which are related to uncharged PAA chains, a second effect, namely decreasing force plateaus (see Figure 7c), occurs. The fact that the plateau forces are equal at zero distance indicate that the underlying mechanism (23) Hackley, V. A. J. Am. Ceram. Soc. 1997, 80, 2315-2325.
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does not depend on the length of the adsorbed segment but on the length of the bridging segment. How this should effect the plateau force is unclear. The resulting negative slopes in Figure 8 suggest the continuous transition as described above.
Conclusions We demonstrated that the adhesion properties of bridging polymers are dependent on the interaction with both surfaces in a differential manner. In the AFM-based single molecule desorption experiments surface end-grafted PAA chains were allowed to adsorb on an AFM-tip and the maximum bridging length was determined upon retracting the cantilever. The impact of the second surface was clearly shown by a manipulation of the polymer surface interaction via changing the pH of the aqueous solution, which led to large differences of the bridging length distributions. The experimental results were found to be in very good agreement with a model for differential polymer adhesion in analogy to the Bell-Evans formalism. The findings are of
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general importance for all applications where polymer bridging occurs but with special impact in the case of similar surface properties. Moreover we showed that the desorption force as a function of the solution pH and thus of the degree of dissociation of the PAA chains depends on the grafting density of the polymer monolayers. The dissociation was reduced at higher grafting density. Differences in the interaction force were also found on the level of individual polymers showing that the desorption force is also depending on the contour length of the polymer chains. Acknowledgment. Helpful discussions with Prof. Thorsten Hugel (TU Mu¨nchen) and Dr. Markus Seitz are gratefully acknowledged. This work was supported by the Deutsche Forschungsgemeinschaft (SFB 486) as well as DAAD and EGIDE (Procope). LA063682Y
